AA all in

Hello,

Live poker table, 8 players, many are loose and not that good. Blinds 1/2, Hero stack 350

Hero AA in SB, button just called straddle (4), h raise 12, UTG called and button called.

Pot ~38
Flop 9♠️ 7♣️ 5♣️

H wants to stop villans to follow any draw (table is loose, so they could have called with some suited connector or A8, A6 or even A9).
Bet 50, both v call

Pot ~200
Turn 9♠️ 7♣️ 5♣️ 3♠️

Now h has less than 300, and this card doesn't help most of the time v, unless one of them has 46, but I think 6 or 8 or ♣️ would have been worse.
Because of some previous hand, one of the villan may call hero all in even if behind following some draw, so h shove on the turn.

What do you think about H strategy?